DES MOINES, Iowa (CNN) -- With two days to go until the Iowa caucuses, a new CNN/Opinion Research Corp. poll out Tuesday shows both the Democratic and Republican presidential nomination races tied at the top.

Hillary Clinton, left, and Barack Obama are in a statistical dead heat in Iowa, according to a new poll.

But with a quarter of all Democratic voters and nearly half of all Republican voters still making up their minds at this late stage, almost anything can happen Thursday night in the first contest for the White House.

Among Democrats, Sen. Hillary Clinton of New York wins the most support, with 33 percent of likely Democratic caucus-goers backing Clinton and 31 percent supporting Sen. Barack Obama of Illinois. But taking into account the survey's sampling error of 4.5 percentage points in the Democratic race, the race is virtually tied.

Former Sen. John Edwards of North Carolina is in third place in the poll at 22 percent.

"Edwards doesn't stand out on any of the qualities, according to poll," said CNN Senior Political Analyst Bill Schneider.

The remaining Democratic presidential candidates, New Mexico Gov. Bill Richardson, Sen. Joe Biden of Delaware, Sen. Chris Dodd of Connecticut and Rep. Dennis Kucinich of Ohio are all in single digits. Former Sen. Mike Gravel of Alaska is at less than 0.5 of 1 percent.

The battle for the GOP presidential nomination is also tied at the top. Former Massachusetts Gov. Mitt Romney has the backing of 31 percent of likely Republican caucus-goers, while 28 percent support former Arkansas Gov. Mike Huckabee. Taking into account the survey's sampling error of 5 percentage points in the GOP race, it's a statistical dead heat between Romney and Huckabee.

Former Sen. Fred Thompson of Tennessee places third in the poll at 13 percent with Sen. John McCain of Arizona 3 points back. Former New York City Mayor Rudy Giuliani is at 8 percent, as is Rep. Ron Paul of Texas.

Rep. Duncan Hunter of California is at less than 0.5 of 1 percent.

Romney gained 6 points since the last CNN poll in Iowa, taken in mid December, with Huckabee dropping 5 points in the same time. Huckabee has lost ground "mostly among higher income Republicans and GOP's under 50 years old," said Holland.

"Romney support has risen entirely among women, where it doubled over the last two weeks," said Schneider.

Meanwhile, a new poll by the Des Moines Register, also out Tuesday morning, suggests the race now has two front-runners: Obama has the support of 32 percent of likely Democratic caucus-goers, with Clinton at 25 percent and Edwards at 24 percent. The poll suggests that an influx of first time caucus-goers, independents, and young voters are contributing to Obama's lead.

In the battle for the GOP nomination, Huckabee leads with the backing of 32 percent of likely Republican caucus-goers, with Romney at 26 percent, McCain at 13 percent and Thompson and Paul at 9 percent.

The newspaper's poll surveyed 800 likely caucus participants between December 27 and 30 and had a sampling error of plus or minus 3.5 percent.

The CNN poll found that when it comes to the issues, the economy, illegal immigration and terrorism continue to dominate the GOP debate, while Iraq remains the No. 1 issue for Democrats with the economy and health care not far behind.

"It's worth emphasizing the amount of caution with which any Iowa poll results should be handled," said Holland. Nearly half of likely Republican caucus-goers say they have not made their minds up; more than a quarter of Democratic caucus-goers say the same thing.

For the Democrats, the caucus winner will be determined by a complicated "post-viability" estimate of something called "delegate equivalents," which is based on voter turnout in the past two general elections. Republican results will be tabulated by a straightforward ballot process.

"Most important, always bear in mind that polls can only do so much when analyzing caucuses which often draw only about 100,000 people out of a statewide population of just under 3 million," added Holland.

The CNN/Opinion Research Corp. Poll was conducted by telephone on December 26-30. There were 482 likely Democratic caucus-goers and 373 likely GOP caucus goers interviewed for the survey.E-mail to a friend